Since she arrived in the United States two months ago, Gislene Batista has been unable to find work and has had no permanent place to live.

But a more pressing issue has consumed her: Getting her 11-year daughter Emily, who has cerebral palsy, access to quality health care.

Batista, who fled her native Brazil to avoid violence against her family, asked lawmakers Tuesday to pass a bill that would allow undocumented children like Emily to receive state-funded health coverage.

Jay Sicklick, deputy director of the Center for Children’s Advocacy, estimated the first-year cost to be $4 million and the second-year expense to be $13 million. He acknowledged that no money has been set aside in Gov. Ned Lamont’s proposed budget for the expansion, and there was no immediate plan to come up with the funds.

“We’re totally realistic in the landscape of the financial situation,” Sicklick said, “and I’m sure the legislators who are interested in this are not immune to the idea that this has got a pretty heavy price tag.”

Still, “we’re optimistic,” he added. “It’s an opportunity to potentially decrease costs down the road. Preventative care for children reaps huge outcomes in the long run. It reduces acute care costs that are going to be borne by acute care hospitals down the road if children who are ineligible for health coverage are then forced into emergency situations.”